// Numbas version: exam_results_page_options
{"name": "W2a: Solve an equation with a reciprocal-1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "variables": {"t": {"group": "Ungrouped variables", "definition": "random(2..8)", "description": "", "templateType": "anything", "name": "t"}, "a": {"group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "name": "a"}, "s2": {"group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "name": "s2"}, "an2": {"group": "Ungrouped variables", "definition": "a*(d-c)", "description": "", "templateType": "anything", "name": "an2"}, "d": {"group": "Ungrouped variables", "definition": "abs(c)+random(2..9)", "description": "", "templateType": "anything", "name": "d"}, "s1": {"group": "Ungrouped variables", "definition": "random(-1,1)", "description": "", "templateType": "anything", "name": "s1"}, "b1": {"group": "Ungrouped variables", "definition": "s1*random(1..10)", "description": "", "templateType": "anything", "name": "b1"}, "an1": {"group": "Ungrouped variables", "definition": "t-b*d+b*c", "description": "", "templateType": "anything", "name": "an1"}, "b": {"group": "Ungrouped variables", "definition": "if(a=abs(b1),abs(b1)+2,b1)", "description": "", "templateType": "anything", "name": "b"}, "c": {"group": "Ungrouped variables", "definition": "s2*random(1..9)", "description": "", "templateType": "anything", "name": "c"}}, "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve for $x$: $\\displaystyle \\frac{a} {bx+c} + d= s$</p>"}, "name": "W2a: Solve an equation with a reciprocal-1", "advice": "<p>Rearrange the equation by adding {-c} to both sides to get:<br/>\\[\\simplify{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\\]<br/>This gives \\[\\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\\] (this is because if $\\displaystyle \\frac{a}{b}=c$ then $\\displaystyle \\frac{b}{a}=\\frac{1}{c}$ on turning the fraction round the other way)<br/>and so \\[\\simplify{({a} * x + {b}) = {t} / {d -c}}\\] on multiplying both sides by {t}.<br/>Hence \\[\\simplify{{a} * x = {t} / {d -c} -{b} = ({a * an1} / {an2})}\\]<br/>and so \\[\\simplify{x={an1}/{an2}}\\] is the solution on dividing both sides by {a}.</p>", "tags": [], "preamble": {"css": "", "js": ""}, "variable_groups": [], "statement": "\n\t    <p>Solve the following equation for $x$.</p>\n\t  <p>Input your answer as a fraction or an integer as appropriate and not&nbsp;as a decimal.</p>\n\t    \n\t    \n\t  \n\t  \n\t", "parts": [{"steps": [{"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "prompt": "\n\t\t\t\t\t            <p>Rearrange the equation by adding {-c} to both sides to get:<br/>\\[\\simplify[std]{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\\]</p>\n\t\t\t\t\t          <p>This gives \\[\\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\\] (this is because if $\\displaystyle \\frac{a}{b}=c$ then $\\displaystyle \\frac{b}{a}=\\frac{1}{c}$ on turning the fraction round the other way)</p>\n\t\t\t\t\t          <p>and so \\[\\simplify{({a} * x + {b}) = {t} / {d -c}}\\] on multiplying both sides by {t}.</p>\n\t\t\t\t\t          <p>Solve this equation for $x$.</p>\n\t\t\t\t\t            \n\t\t\t\t\t            \n\t\t\t\t\t          \n\t\t\t\t\t          \n\t\t\t\t\t", "useCustomName": false, "scripts": {}, "marks": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "adaptiveMarkingPenalty": 0, "type": "information", "customName": "", "unitTests": []}], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"valuegenerators": [], "variableReplacements": [], "scripts": {}, "marks": 3, "checkVariableNames": false, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "checkingAccuracy": 0.0001, "adaptiveMarkingPenalty": 0, "type": "jme", "unitTests": [], "answer": "{an1}/{an2}", "vsetRangePoints": 5, "showPreview": true, "notallowed": {"showStrings": false, "strings": ["."], "partialCredit": 0, "message": "<p>Input as a fraction or an integer, not as a decimal.</p>"}, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "answerSimplification": "std", "showCorrectAnswer": true, "showFeedbackIcon": true, "vsetRange": [0, 1], "failureRate": 1, "customName": ""}], "showCorrectAnswer": true, "prompt": "\n\t\t\t      <p>\\[\\simplify{{t} / ({a} * x + {b}) + {c} = {d}}\\]</p>\n\t\t\t        <p>$x=\\;$ [[0]]</p>\n\t\t\t        <p>If you want help in solving the equation, click on \"Show steps\". If you do so then you will lose 1 mark.</p>\n\t\t\t        <p>Input all numbers as fractions or integers and not as decimals.</p>\n\t\t\t      \n\t\t\t", "useCustomName": false, "scripts": {}, "marks": 0, "sortAnswers": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "stepsPenalty": 1, "customMarkingAlgorithm": "", "adaptiveMarkingPenalty": 0, "type": "gapfill", "customName": "", "unitTests": []}], "extensions": [], "ungrouped_variables": ["a", "c", "b", "d", "s2", "s1", "b1", "t", "an2", "an1"], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}